Chebycheff and Belyi Polynomials, Dessins d’Enfants, Beauville Surfaces and Group Theory

We start discussing the group of automorphisms of the field of complex numbers, and describe, in the special case of polynomials with only two critical values, Grothendieck’s program of ‘Dessins d’ enfants’, aiming at giving representations of the absolute Galois group. We describe Chebycheff and Belyi polynomials, and other explicit examples. As an illustration, we briefly treat difference and Schur polynomials. Then we concentrate on a higher dimensional analogue of the triangle curves, namely, Beauville surfaces and varieties isogenous to a product. We describe their moduli spaces, and show how the study of these varieties leads to new interesting questions in the theory of finite (simple) groups. We would like to thank Fabio Tonoli for helping us with the pictures.     

Chemisorption of atomic hydrogen in graphite and carbon nanotubes

An orthogonal tight-binding model of the carbon-hydrogen interaction was modified to deal with the different hybridization states of atomic hydrogen on carbon surfaces, without explicitly including charge self-consistency. The resulting model has great flexibility and computational efficiency, generally with a good quantitative accuracy. The non-self-consistent C-H model was tested by calculating structural properties of small hydrocarbons and simple polymers, and against ab initio results of H binding to both perfect and defective graphite. The model was employed to study the chemisorption properties and dynamics of atomic hydrogen on perfect and defective surfaces of graphite and carbon nanotubes.     

Kinetic and thermodynamic study of the Na4(UO2)2(OH)4(C2O4)2 complex

The synthesis, the characterization, and the thermal decomposition of the dioxouranium(VI) ternary complex of formula Na₄(UO₂)₂(OH)₄(C₂O₄)₂, has been studied. The identification of the compound was performed by chemical analysis and by infrared spectrometry. Thermal decomposition of the compound occurs in several steps due to the decomposition of the salt to Na₂O and UO₃ oxides. The stoichiometry of the steps, hypothesized by means of the thermodynamic and kinetic parameters, is confirmed by the evolved gas analysis studied by FTIR spectrometer coupled to TG/DSC apparatus. Model‐fitting and model‐free kinetic methods have been used in kinetic analysis. The latter allows determining kinetic scheme. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 35: 661–669, 2003     

A coupled interface-multilayer approach for mixed mode delamination and contact analysis in laminated composites

An accurate laminate model developed by using multilayer shear deformable plate modeling and interface elements, based on fracture mechanics and contact mechanics, is proposed to analyze mixed mode delamination in composite laminates. Perfect adhesion along the undelaminated portion of the delamination plane is simulated by treating interface stiffnesses as penalty parameters, whereas to enforce interface displacement continuity between plate elements constituting each sub-laminate above or below the delamination plane, the Lagrange multiplier method is used. The governing differential equations are derived through a variational procedure by using a modified total potential energy functional. Results are obtained by numerical integration of the non-linear three-point boundary value problem modeling mixed-mode delamination of the laminate plate subjected to end loading, which accounts also for the frictionless contact condition.The coupling of a penalty procedure with the Lagrange multiplier method, results in an accurate and direct energy release rate evaluation. Comparisons with results available from the literature obtained with a local continuum approach, show that mode partition may be performed to the desired accuracy by refining multilayer plate models for each sub-laminate. In addition, original analytical formulas for mode partition are obtained by coupling the interface approach and fracture mechanics concepts, evidencing the effectiveness of the proposed approach and gaining a better insight into the influence of shear effects on mode decomposition. Numerical computations for practical problems, evidence both the relative simplicity and the efficiency of the proposed model to represent mixed mode interlaminar fracturing as well as crack–face interaction.     

First‐principle modelling of forsterite surface properties: Accuracy of methods and basis sets

The seven main crystal surfaces of forsterite (Mg₂SiO₄) were modeled using various Gaussian‐type basis sets, and several formulations for the exchange‐correlation functional within the density functional theory (DFT). The recently developed pob‐TZVP basis set provides the best results for all properties that are strongly dependent on the accuracy of the wavefunction. Convergence on the structure and on the basis set superposition error‐corrected surface energy can be reached also with poorer basis sets. The effect of adopting different DFT functionals was assessed. All functionals give the same stability order for the various surfaces. Surfaces do not exhibit any major structural differences when optimized with different functionals, except for higher energy orientations where major rearrangements occur around the Mg sites at the surface or subsurface. When dispersions are not accounted for, all functionals provide similar surface energies. The inclusion of empirical dispersions raises the energy of all surfaces by a nearly systematic value proportional to the scaling factor s of the dispersion formulation. An estimation for the surface energy is provided through adopting C₆ coefficients that are more suitable than the standard ones to describe O? O interactions in minerals. A 2 × 2 supercell of the most stable surface (010) was optimized. No surface reconstruction was observed. The resulting structure and surface energy show no difference with respect to those obtained when using the primitive cell. This result validates the (010) surface model here adopted, that will serve as a reference for future studies on adsorption and reactivity of water and carbon dioxide at this interface. © 2015 Wiley Periodicals, Inc.     

Minimum principles,convexity, and thermodynamics in viscoelasticity

A linear viscoelastic solid is considered along with the complete set of thermodynamic restrictions on the relaxation function. It is shown that such reslrictions imply the validity of a dissipativity condition, so far regarded as unrelated to the second law. Next it is remarked that the thermodynamic restrictions imply the convexity of a commonly used bilinear functional and the stationarity only if the class of displacement field is appropriate. Then it is proved that the Laplace transform of the solution to the mixed problem gives the strict minimum of a bilinear functional and vice versa. Finally, a bilinear functional with a weight function is considered and it is shown that the solution to the mixed problem gives the strict minimum and vice versa.     

Maximum recoverable work and pseudofree energies for a rigid heat conductor

In this paper, we consider a linear theory for a rigid heat conductor with memory effects for a heat flux in order to deduce explicit formulas for the minimum free energy, which is related to the maximum recoverable work that can be obtained from a given state of a body. Two equivalent forms of this work are given in the frequency domain. Finally, two different expressions for a thermodynamic potential, called pseudofree energy, are introduced for this material. Published in Neliniini Kolyvannya, Vol. 10, No. 1, pp. 7–25, January–March, 2007.     

Objective Bayesian modelling of insurance risks with the skewed Student‐t distribution

Insurance risks data typically exhibit skewed behaviour. In this paper, we propose a Bayesian approach to capture the main features of these data sets. This work extends a methodology recently introduced in the literature by considering an extra parameter that captures the skewness of the data. In particular, a skewed Student‐t distribution is considered. Two data sets are analysed: the Danish fire losses and the US indemnity loss. The analysis is carried with an objective Bayesian approach. For the discrete parameter representing the number of the degrees of freedom, we adopt a novel prior recently appeared in the literature. Copyright © 2017 John Wiley & Sons, Ltd.